Question

Anita has borrowed $1,000 on which interest is charged at 6% effective.Anita is accumulating a sinking fund at 4% effective to repay the loan.At the end of 5 years, the balance in the sinking fund is $587.82.At the end of the 6^th year, Ada makes a total payment of $168.53.

(a) How much of the $168.53 pays interest currently on the loan?

(b) How much of the $168.53 goes into the sinking fund?

(c) How much of the $168.53 should be considered as net interest?

(d) How much of the $168.53 should be considered as principal?

(e) What is the sinking fund balance at the end of the 6^th year?

Answer 1

Following are the answers with most appropriate logics for the above questions:

(a) Loan principal will remain $1,000, because payments have been in sinking fund, therefore, Interest currently paid on loan is,

=Borrowed Loan * Effective rate of interest

= $1,000 * 6%

= $60

(b) Out of $168.53, amount paid as interest ($60) and balance will goes to sinking fund i.e.

= $168.53 - $60

= $108.53

(c) Now, out of $168.53, effective net interest will be,

= Effective interest paid - Interest earned on Sinking fund

= $60 - $23.5128 (WN)

= $ 36.4872

WN : Interest earned on Sinking Fund = Balance of Sinking fund at the end of 5th year * Effective rate to repay loan

= $587.82 * 4% = $23.5128

(d) Total payment consist of principal and net interest, therefore,

Total Payment = Principal + Net Interest

$ 168.53 = Principal + $36.49

Therefore, Principal = $132.04

(e) Sinking Fund balance at the end of 6th year will be,

= (Balance at the end of 5th year * Effective rate to repay loan) + new amount gone to Sinking Fund

= ($587.82 * 1.04) + 108.53

= $719.8628

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